A large number n of blood samples are to be screened for HIV. Testing each and every sample separately needs n tests. Pooling half of each sample needs one test if all samples are free from HIV, while if at least one is defective, the other half of each sample could be tested individually. Most of time, we might get away with doing just one test. Let p denote probability that an individual test is negative. And let X denote total number of tests required. How many tests should the technician expect to do? Describe all your work and clearly state any assumptions you make or any rules you use.